Bounds for the blowup time of the solutions to quasi-linear parabolic problems

The relationships between some types of partial differential equations and ordinary differential equations as well as their applications

“…Since we hope to obtain the bounds for the blowup time t ∗ of u ( x , t ), we are only concerned with in the case of p >1. Similar to Bao and Song and Lv and Song, we will obtain the upper bound for the blowup time to the solution by constructing subsolution. Let λ >0 be the first eigenvalue of and φ be the corresponding eigenfunction satisfying that φ ( x )>0 in Ω and .…”

“…Since we hope to obtain the bounds for the blowup time t * of u(x, t), we are only concerned with (5) in the case of p > 1. Similar to Bao and Song 26 and Lv and Song, 27 we will obtain the upper bound for the blowup time to the solution by constructing subsolution. Let > 0 be the first eigenvalue of…”

“…We would like to compare our methods with others. There are many results about the topic on the bounds for blowup time of the solution to a parabolic equation, we can refer to previous studies [26][27][28][29][30][31][32][33] and the references therein. Differing from the methods in these references, to establish the lower and upper bounds for the blowup time of the solutions to these problems above, we will establish some relationships between these partial differential equations and some ordinary differential equations.…”

Bounds for the blow-up time of a porous medium equation with weighted nonlocal source and inner absorption terms

“…Bao and Song [21] considered the initial boundary value problem of quasilinear parabolic equation under homogeneous Dirichlet or Neumann boundary condition, and the slow diffusion case with nonlocal source term was also included in their results. Besides, one can refer to [22][23][24][25][26][27] for the results about scalar equation with time-dependent coefficients, nonlocal reaction systems, and models of quasilinear equations.…”

Estimates for the blowup time of a combustion model with nonlocal heat sources

“…Consequently, we always assume that r > 1 or p > 1 or sq > (1 − r)(1 − p) in this paper. About the issue on the bounds for the blowup time of the solution to the problem of a single parabolic equation, we can refer to [1,7,11,13,14,15,16,17,18] and the reference therein. However, there are only a little results about the bounds for the blowup time of to a parabolic system.…”